Rationale

Delete §5.3.2 in its entirety, including the simplified gravity formula (Eq 2), the associated nomenclature, and the existing Note 1. Replace the existing Note 1 with new commentary applicable to the force equation in §5.3.1. Current wording (§5.3.2 and Note 1): §5.3.2 provides a simplified formula for calculating local acceleration due to gravity g as a function of latitude Ø and elevation h above sea level (Eq 2), with an associated nomenclature block defining each variable. Note 1 explains that the formula is a simplification of the World Geodetic System 84 Ellipsoidal Gravity Formula, claims accuracy of better than 0.0005 % relative to the full formula, and adds a 0.003 % correction factor associated with assumed rock density of 2.67 g/cm³. Proposed change: Delete §5.3.2 in its entirety, including the gravity formula equation, the nomenclature for g, Ø, and h, and the existing Note 1. Renumber subsequent sections accordingly. Insert a new Note 1 after §5.3.1 reading as follows: Note 1—Two factors in Eq 1 require care. (1) M is the true mass of the weight, where mass is the invariant scalar property of the weight, expressed in kilograms, and does not change with location; the force the weight produces depends on the local acceleration due to gravity at the site of use, so M in Eq 1 is the same regardless of where the weight is used while g must be the local value at the calibration site; not the conventional mass reported on most mass calibration certificates; conventional mass should be converted to true mass before the force is calculated. (2) g is the local acceleration due to gravity at the site of use and varies across the surface of the Earth by approximately 0.5 % between the equator and the poles; g should be obtained for the calibration site, calculated to within 0.0001 m/s² (10 milligals), from the National Geodetic Information Center, National Oceanic and Atmospheric Administration, or by direct gravimetric measurement at the site. Rationale: The simplified gravity formula in §5.3.2 returns theoretical normal gravity for an idealized ellipsoidal Earth; it does not return the actual local gravity at the site of use. Real local gravity differs from the theoretical normal value by gravity anomalies that vary spatially and that are not captured by latitude and elevation alone. The 0.0005 % accuracy claim in the existing Note 1 refers only to the agreement of the simplified formula with the full WGS-84 ellipsoidal formula that is, agreement between two theoretical normal-gravity calculations not to agreement between the formula and the true local gravity. The 0.003 % rock-density caveat in the second half of the existing note further illustrates that the formula is incomplete: it depends on assumptions about subsurface mass distribution that are not generally known to the user. Laboratories targeting expanded uncertainties below approximately 100 ppm of applied force cannot rely on a formula whose total uncertainty contribution is not bounded. The replacement Note 1 directs the laboratory to obtain g from the National Geodetic Information Center (which provides gridded local gravity data accounting for measured anomalies) or by direct gravimetric measurement at the site, both of which produce true local gravity rather than theoretical normal gravity. The new note also distinguishes mass from force: mass is invariant and the same value is entered into Eq 1 regardless of where the weight is used, while the resulting force varies with the local acceleration due to gravity. Conflation of the two is a recurring error mode that the replacement note addresses directly. The first sentence of the new note also addresses the most common error mode in calculating force from mass: laboratories using the conventional mass value reported on the mass calibration certificate without converting it to true mass. Conventional mass is defined per OIML D28 against a reference material of density 8.0 g/cm³ in air of density 0.0012 g/cm³ at 20 °C, and differs from true mass by amounts that depend on the weight material and on the air density convention used; the difference is significant for laboratories targeting expanded uncertainties below approximately 100 ppm of applied force. Removal of §5.3.2 also enables alignment with the single-equation pattern used in ASTM E74 §6.1, which provides one force equation and refers the user to NOAA for g rather than supplying a simplified formula. The existing E2428 equation in §5.3.1 (Eq 1) is retained without modification.